Electronic multipoles in second harmonic generation and neutron scattering

Laan, G. van der; Lovesey, S. W.

doi:10.1103/physrevb.103.125124

Cited by 9 publications

(6 citation statements)

References 64 publications

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“…SHG fundamentally arises from symmetry breaking in the second-order susceptibility, making it a powerful tool for imaging crystal lattices with symmetry breaking, such as ferroelectrics (30). Moreover, CD in SHG is an established technique to probe chirality (31)(32)(33)(34) and can result from, for instance, chiral ordering of electric dipoles or the existence of ferromagnetism (35,36). The lack of magnetism in PTO and STO suggests that any SHG-CD that arises must come from a chiral ordering of dipoles.…”

Section: Resultsmentioning

confidence: 99%

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Electric field control of chirality

et al. 2022

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Polar textures have attracted substantial attention in recent years as a promising analog to spin-based textures in ferromagnets. Here, using optical second-harmonic generation-based circular dichroism, we demonstrate deterministic and reversible control of chirality over mesoscale regions in ferroelectric vortices using an applied electric field. The microscopic origins of the chirality, the pathway during the switching, and the mechanism for electric field control are described theoretically via phase-field modeling and second-principles simulations, and experimentally by examination of the microscopic response of the vortices under an applied field. The emergence of chirality from the combination of nonchiral materials and subsequent control of the handedness with an electric field has far-reaching implications for new electronics based on chirality as a field-controllable order parameter.

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Section: Resultsmentioning

confidence: 99%

“…⊗ .} K denotes a standard tensor product of rank K, C 2 (R) is a spatial spherical harmonic of rank 2 normalized such that C 1 (R) = R. The corresponding energy-integrated MCD signal is a correlation of orbital angular momentum and space, specifically, a sum of multipoles {C 2 (R) ⊗ L} K with K = 1 and 3 36.…”

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Electric field control of chirality

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“…Specifically, D = (1/2)[3(h 1 ) (S×R) − ( j 0 ) + (g 1 ) (iR) ]. Form factors (h 1 ), ( j 0 ) and (g 1 ) have been calculated for several atomic configurations [32,33]. In what follows, we retain D and a quadrupole H 2 that possess the largest atomic form factors.…”

Section: Magnetic Neutron Diffractionmentioning

confidence: 99%

Hidden magnetic order on a kagome lattice for KV3Sb5

Scagnoli

Khalyavin²,

Lovesey

2022

Phys. Rev. B

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KV 3 Sb 5 has recently attracted considerable attention due to its low-temperature superconducting properties, which are heralded by a charge-density wave. The apparent presence of a very weak magnetism does not result in long-range ordering. An explanation of the properties we present invokes higher-order terms in the vanadium magnetization density and a "hidden order" of Dirac (polar) multipoles. The Dirac dipole, known as an anapole or toroidal dipole, is one of a family of electronic multipoles visible in x-ray and magnetic neutron diffractions while undetectable with standard laboratory-based techniques. Actually, two viable magnetic structures, direct descendants of the established chemical structure, are studied with a view to testing their suitability in future experiments. One model structure is magnetoelectric and restricted to the linear type, whereas a second model cannot show a magnetoelectric effect of any type. The latter hosts a strange vanadium entity that is a true scalar and magnetic (time-odd), and associated in our paper with a fictitious charge distribution that is purely imaginary. Calculated x-ray and neutron-scattering amplitudes are symmetry-informed expressions of vanadium Dirac multipoles. Bragg diffraction patterns for the two models are found to be distinctly different, fortunately. Likewise, magnetochiral signals derived from our x-ray scattering amplitudes.

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“…The identity (J||T K ||j) = (−1) j + J (−1) K (j||T K ||J) is valid for parity-even multipoles [33].…”

Section: Appendix Bmentioning

confidence: 99%

Bragg diffraction by a magnetic all-in-all-out configuration with application to a cubic cerium pyrochlore oxide

Lovesey¹

2022

Preprint

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The Bragg diffraction of neutrons and x-rays are well-suited to the task of determining the distribution of magnetization in crystals. Applications of the two techniques proceed by contrasting observed intensities with intensities calculated with a specific model, and changing the model as need be to achieve satisfactory agreement. An all-in-all-out (AIAO) magnetic configuration of magnetic dipoles on a cubic face-centred lattice with networks of corner-sharing tetrahedra is often mentioned in the context of pyrochlore oxides, for example, but the corresponding neutron and x-ray diffraction patterns appear not have been calculated. Our results for patterns of Bragg spots from an AIAO magnetic configuration defined by a magnetic space group are symmetry informed and yield exact reflection conditions. Specifically, a long-range order of magnetic dipoles is forbidden in our model. Bulk properties arise from higher-order multipoles that include quadrupoles and octupoles. Bragg spots that exclude all magnetic multipoles other than an octupole have been discovered, and they can be observed by both neutron diffraction and resonant x-ray diffraction. All magnetic multipoles allowed in diffraction by cerium ions (4f 1 ) are presented in terms of coefficients in a welldocumented and unusual magnetic ground state. Symmetry of the cerium site in the cubic structure constrains the coefficients. Our scattering amplitudes have an application in both neutron and x-ray diffraction experiments on Ce2Zr2O7, for example, and searches for the sought-after cerium octupole. Also presented for future use is a result for the total, energyintegrated magnetic neutron scattering intensity by a powder sample.

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Electronic multipoles in second harmonic generation and neutron scattering

Cited by 9 publications

References 64 publications

Electric field control of chirality

Electric field control of chirality

Hidden magnetic order on a kagome lattice for KV3Sb5

Bragg diffraction by a magnetic all-in-all-out configuration with application to a cubic cerium pyrochlore oxide

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